In conventional die-cutting and scoring of packaging material, cutting knives and/or scoring rules disposed in a punch are thrust at high speed directly against the unprotected packaging material which is squeezed between the die-cutting/scoring tools and an anvil consisting of either a flat plate (planar die-cutting and scoring) or a rotating cylinder (rotary cutting and scoring). In the latter case, also the cutting/scoring tools are disposed on a rotating cylinder. The cutting knives produce a complete penetration of the packaging material, i.e. a division thereof, whereas the scoring rules which do not penetrate the packaging material completely, produce a permanent deformation and a weakening of the flexural rigidity, i.e. fold lines. Crack-producing forces arise in the packaging material in the direction of its plane, both where complete and incomplete penetration occurs. With present-day technique, these forces often are the cause of an annoying formation of cracks, so that higher grammage, greater strength or thickness of the packaging material is required than would otherwise be necessary. The risk of crack formation increases production costs and restricts the construction possibilities of the packages. In extreme cases, die-cutting and scoring techniques cannot be used at all.